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3 years ago

Three times one number minus another number equals 34. If the sum of the numbers is 22, what are the two numbers?

Mathematics

1 answer:

lubasha [3.4K]3 years ago

8 0

Answer:

8 and 14

Step-by-step explanation:

let the 2 numbers be x and y with x > y

We can model the situation using the following 2 equations

x + y = 22 → (1)

3x - y = 34 → (2)

adding the equations term by term will eliminate the term in y

(x + 3x) + (y - y) = (22 + 34)

4x = 56 ( divide both sides by 4 )

x = 14

substitute x = 14 into (1)

14 + y = 22 ⇒ y = 22 - 14 = 8

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Complete the work to find the dimensions of the rectangle. x(x – 3) = 10 x2 – 3x = 10 x2 – 3x – 10 = 10 – 10 (x + 2)(x – 5) = 0

Norma-Jean [14]

Answer:

$Length =5$

$Width = 2$

Step-by-step explanation:

Given

$Length =x$

$Width = x -3$

$Area = 10$

$x(x-3) =10$

See comment for missing part of the question

Required

Complete the expression to determine the dimension of a rectangle

We have:

$x(x-3) =10$

Open bracket

$x^2 -3x = 10$

Equate to 0

$x^2 -3x - 10 =0$

Expand

$x^2 + 2x - 5x - 10 = 0$

Factorize

$x(x + 2) - 5(x + 2) = 0$

Factor out x + 2

$(x - 5)(x + 2) = 0$

Solve for x

$x - 5 = 0$ or $x + 2 = 0$

$x = 5$ or $x = -2$

The value of x cannot be negative

So:

$x = 5$

Recall that:

$Length = x$

$Width = x - 3$

So:

$Length =5$

$Width = 2$ ---- i.e. 5 - 3

6 0

2 years ago

The sum of the measures of the angles of a triangle is 180°. The middle-sized angle measures 3° more than 2 times the smallest a

Anit [1.1K]

Answer:

13° , 29° , 138°

Step-by-step explanation:

let x be the smallest angle , then

2x + 3 is the middle angle and

2x + 3 + 109 is the largest angle

summing the 3 angles and equating to 180

x + 2x + 3 + 2x + 3 + 109 = 180 , that is

5x + 115 = 180 ( subtract 115 from 180 )

5x = 65 ( divide both sides by 5

x = 13

2x + 3 = 2(13) + 3 = 26 + 3 = 29

2x + 3 + 109 = 29 + 109 = 138

the 3 angles are 13° , 29° , 138°

6 0

1 year ago

Elimination method - -4x = 4y<br> 4x - 8y = 12

nika2105 [10]

Answer: (4,-4)

y=-4, x=4

Step-by-step explanation:

-4x=4y

4x-8y=12

-8y=-4x+12 Now I can substitute -4x for 4y

-8y=4y+12

-2y=y+12

-3y=12

y=-4

-4x=4y

-4x=4(-4)

x=4

6 0

3 years ago

Madison is buying a $3,000 car at 9% simple interest for 2 years. What will be the total amount she pays for the car?

zmey [24]

The answer to the question is 18$

3 0

2 years ago

Read 2 more answers

X^2 - (x-y)^2 •y. If x = -5 and y = -8

ki77a [65]

Equation: x² - (x - y)² * y

Substitute values for x and y into equation.

-> (-5)² - ( (-5) - (-8) )² * (-8)
-> 25 - (-5 + 8)² * (-8)
-> 25 - (3)² * (-8)
-> 25 - 9 * (-8)
-> 25 - (-72)
-> 25 + 72
-> 97

3 0

2 years ago